(analysis, of a function) Such that, for every x in the domain, for each small openintervalD about f(x), there's an interval containing x whose image is in D.

(mathematics, more generally, of a function) Such that each open set in the range has an open preimage.

Each continuous function from the real line to the rationals is constant, since the rationals are totally disconnected.

(grammar) Expressing an ongoing action or state.

Usage notes

Continuous is stronger than continual. It denotes that the continuity or union of parts is absolute and uninterrupted, as in a continuous sheet of ice, or a continuous flow of water or of argument. So Daniel Webster speaks of "a continuous and unbroken strain of the martial airs of England." By contrast, continual usually marks a close and unbroken succession of things, rather than absolute continuity. Thus we speak of continual showers, implying a repetition with occasional interruptions; we speak of a person as liable to continual calls, or as subject to continual applications for aid.

Sentence Examples

This girl's code, if it is in fact a code, is mostly one continuous line, with hardly any punctuation.

All he sees is one continuous line.

Moreover, small particles do not seem to exist in the water until it is broken up; so far as we can see, the material of the water is continuous not granular.

This conception of matter, as infinitely divisible and continuous, was taught by Anaxagoras more than four centuries before the Christian era, and in the philosophy of Aristotle the same ideas are found.

This enormous capacity for expansion and contraction is astonishing if we believe matter to be continuous, but if we imagine air to be made up of little particles separated by relatively large empty spaces the changes in volume are more easily conceivable.

Synonyms

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Most activist Muslims, like me, will always fight to protect Jews from anti-Semitism but will always fight the racist and apartheid goals of Zionism. Zionism requires a continuous shrill cacophony in the background, for it requires the suspension of reason in asserting that an end goal for one people can be justified by any means against another. Akber Choudhry